Efficient Frequency-Domain Analysis of PEEC Circuits Through Multiscale Compressed Decomposition

The solution of mixed electromagnetic/circuit problems is important for the electromagnetic compatibility/signal integrity/power integrity system designs. The ever-increasing frequency content of signals and decrease of geometrical features requires the 3-D electromagnetic methods, such as the partial element equivalent circuit (PEEC) method, to be used for the analysis and design of high-speed circuits. Very large systems of equations are often produced and their efficient solution can be extremely challenging. In this paper, we propose a new frequency-domain PEEC solver which is based on the adaptive cross approximation and singular value decomposition. Taking advantage of the rank deficiency of the dense partial inductance and coefficient of potential matrices, a multiscale block decomposition is adopted to explicitly compute the inverse of the admittance matrix of the PEEC circuit. The proposed approach provides both speedup and memory storage saving, while preserving the accuracy. The efficiency of the proposed method is demonstrated through its application to the PEEC modeling of typical interconnect problems.